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During a science experiment, Cesar sets up a group of filter that removes contaminants from a liquid sample. Each filter removes 94.8% of the remaining contaminants. Which recursive formula describes the fraction of contaminants still remaining in the liquid sample after passing through n filters?

Respuesta :

Using an exponential function, the recursive formula that describes the fraction of contaminants still remaining in the liquid sample after passing through n filters is given by:

[tex]A[n] = (0.052)^n[/tex]

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem, considering an initial fraction of A(0) = 100% = 1, the decay rate is of r = 0.948, hence the formula is:

[tex]A[n} = (1 - r)^n[/tex]

[tex]A[n] = (0.052)^n[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

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